You are playing a game with three cards. At the start, all three cards are face down. You know that a different real number is written on every card, but you do not know what the numbers are. The rules of the game are as follows: You can choose any card and turn it over (assuming that you have not already turned it over). You can either keep the card, or discard it. If you discard a card, then you cannot go back to it; you must choose a new card. If the card you have kept has the largest real number on it, then you win the game. If you use the optimal strategy, then what is the probability that you win the game

Answers

Answer 1

concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.

How to find the probability?

Now, we know that there are 52 cards in a normal deck, if we only keep the ones with real numbers, there are 40.

These numbers go from 1 to 10.

5.5 is the average real number in the cards, so, having a 6 or more in a card is what we expect.

This means that if the card that we turn up is smaller than 6, we discard it.

If the card has the value 6 or larger, we keep it.

In this case, the probability of losing is if one of the other cards has a value larger than 6.

The probability that a random card has a value larger than 6 is:

p = (number of cards with a value larger than 6)/(total number of cards)

p = (16/39)

(The quotient is 39 instead of 40, because we already know one of the cards)

This means that if keep the 6, the probability of winning is:

1 - 16/39 = 0.59

If instead, we got a 7, obviously we keep it, in that case the probability of winning is:

1 - 12/39 = 0.69

And so on, concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.

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Related Questions

The voice onset time (vot) for the sound /da/ is 17 ms, and the vot for the sound /ta/ is 91 msec. When a computer produces a sound with a vot of 65 ms, listeners are likely to report hearing?

Answers

The the /ta/ sound is the sound which listeners are likely to report hearing. The option B is correct option.

According to the statement

we have given that the The voice onset time (vot) for the sound /da/ is 17 ms, and the vot for the sound /ta/ is 91 msec. and we have to find the sound which listeners are likely to report hearing.

So, For this purpose, we know that the

Traffic announcement (TA) refers to the broadcasting of a specific type of traffic report on the Radio Data System. It is generally used by motorists, to assist with route planning, and for the avoidance of traffic congestion.

And according to this and the voice onset time is

The brief instant that elapses between the initial movement of the speech organs as one begins to articulate a voiced speech sound and the vibration of the vocal cord.

And according to this

the /ta/ sound is the sound which is the like by the listeners are likely to report hearing.

So, The the /ta/ sound is the sound which listeners are likely to report hearing. The option B is correct option.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

The voice onset time (VOT) for the sound /da/ is 17 ms, and the VOT for the sound /ta/ is 91 msec. When a computer produces a sound with a VOT of 65 msec, listeners are likely to report hearing

a. the /da/ sound

b. the /ta/ sound

c. the /ja/ sound

d. a combination of /ta/ and /da/

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Of the following, which reads the same forwards, backwards, and upside down (when viewed on a calculator screen)?
(A) 6889
(B)1991
(C)1961
(D) 1881

Answers

Answer: D 1881

Step-by-step explanation: 6889 and 1961 don't read the same forwards and backward. 1991 upside down is 1661. So, only 1881 works

What is the sign of b/c

Answers

Answer:

Negative.

Step-by-step explanation:

b is above zero. So, it is positive.

c is below zero. So, it is negative.

A positive divided by negative number results in negative.

Answer:

B. negative

Step-by-step explanation:

-2 is negative. That's why.

To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create an inequality in standard form that represents the restaurant owner’s desired revenue.

Type the correct answer in each box. Use numerals instead of words.

Answers

The inequality in the box has to be written as

x² + 2x - 80 ≤ - 65

How to solve the inequality

We have

(10 + x)1 * (16-2x) ≥ 130

Next we would have to open the bracket

160 + 16x - 20x - 2x² ≥ 130

Then we would have to arrange the equation

- 2x² - 4x + 160 ≥ 130

Divide the equation by two

- x² - 2x + 80 ≥ 65

This is arranged as

x² + 2x - 80 ≤ - 65

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Find the taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that rn(x) → 0. ] f(x) = 8/x, a = −4

Answers

The taylor series for the f(x)=8/x centered at the given value of a=-4 is -2+2(x+4)/1!-24/16 [tex](x+4)^{2}[/tex]/2!+...........

Given a function f(x)=9/x,a=-4.

We are required to find the taylor series for the function f(x)=8/x centered at the given value of a and a=-4.

The taylor series of a function f(x)=[tex]f(a)+f^{1}(a)(x-a)/1!+ f^{11}(a)(x-a)^{2} /2! +f^{111}(a)(x-a)a^{3}/3!+..........[/tex]

Where the terms in f prime [tex]f^{1}[/tex](a) represent the derivatives of x valued at a.

For the given function.f(x)=8/x and a=-4.

So,f(a)=f(-4)=8/(-4)=-2.

[tex]f^{1}[/tex](a)=[tex]f^{1}[/tex](-4)=-8/([tex]-4)^{2}[/tex]

=-8/16

=-1/2

The series of f(x) is as under:

f(x)=f(-4)+[tex]f^{1}(-4)(x+4)/1!+ f^{11}(-4)(x+4)^{2}/2!.............[/tex]

[tex]=8/(-4)-8/(-4)^{2} (-4)(x+4)/1!+ 24/(-4)^{3} (-4)(x+4)^{2}/2!.............[/tex]

=-2+2(x+4)/1!-24/16 [tex](x+4)^{2}[/tex]/2!+...........

Hence the taylor series for the f(x)=8/x centered at the given value of a=-4 is -2+2(x+4)/1!-24/16 [tex](x+4)^{2}[/tex]/2!+...........

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1. Ansley meets her fruends at the movie theter. They had already purchased a bucket of popcorn, and there is only 3/4 left. Ansley eats 1/3 of the remaining popcorn. How much of the bucket did Ansley eat?

2. Jamie bought 6 pool floats to use during the summer. 2/3 of the floats were tellow. How many yellow floats did he buy?

3. Mrs. Jones purchases 2/3 of a pound of cookies for her class. If the cookies are $6.00 per pound, how much did she pay for the cookies?

4.The school band has 24 members. If 1/8 of them play the drums how many members of the band play the drums?

5. Callie spent 1 1/2 hours outside with her sister. They spent half of theat time jumping on their trampoline. How long did they jump on the trampoline?

Answers

1.   he ate 1/4 of the bucket

2.   4 of the pool floaties are yellow.

3.   she paid 4$ for the cookies

4 .  3 members of the band play the drums

5.   45 minutes

 

Answer:

1.  Ansley eats 1/4 of the popcorn bucket

2. He bought 4 yellow floats

3. She pays 4 pounds for the cookies

4. 3 members of the band play the drums

5. They spent 45 minutes jumping on the trampoline

Step-by-step explanation:

If you would like the explanation, I can comment it below (≧∇≦)/ xx

Hope this helps! ♡

find the surface area of composite figure. use 3.14 for π. round to the nearest tenth

Answers

Answer:

  334 in²

Step-by-step explanation:

The total surface area of the composite figure is the sum of the total area of the bottom cuboid and the lateral area of the top cuboid.

Total cuboid area

The area of a cuboid is given by the formula ...

  A = 2(LW +H(L+W))

For the bottom cuboid, the area is ...

  A = 2((9 in)(7 in) +(5 in)(9 in +7 in)) = 2(63 in² +5(16) in²) = 286 in²

Lateral area

The lateral area of a cuboid is the product of its perimeter and height. The perimeter is the sum of side lengths, or twice the sum of length and width.

  LA = Ph = (2(l +w))h

  LA = 2(5 in +3 in)(3 in) = 48 in²

Total composite area

The total surface area is the sum of the lateral area of the top cuboid and the total area of the bottom cuboid:

  SA = (48 in²) +(286 in²) = 334 in²

The surface area of the composite figure is 334 square inches.

__

Additional comment

The exposed area of the bottom cuboid is its total area less the area of the very top face.

The exposed area of the top cuboid is its lateral area plus the area of the very top face.

When we add these two exposed areas together, we find the area of the very top face is both subtracted and added from the sum of the total bottom area and the lateral top area. We skipped that step of adding and subtracting, because its net effect is zero.

A train traveled 1/5 of the distance between two cities in ¾ hour. at this rate, how many hours will it take the train to travel the entire distance between these two cities?

Answers

Answer:

3 3/4 hour

Step-by-step explanation:

(3/4) ÷ (1/5) = (3*5) / (4*1)

= 15/4 hour

15/4 = 12/4 + 3/4 = 3 + 3/4 hour

= 3 3/4 hour

Ram sold to Shyam an article with 20% profit. Shyam sold same article for Rs. 504 with 5% profit to Ghanashyam. How much did it cost for Ram?
please do this with solutions quickly!!​

Answers

Answer:

Rs 400 is the cost of an article for Ram.....

Step-by-step explanation:

X - cost of an article for Ram

120% = 1.2

1.2*X - Ram’s selling price

5% = 0.05

1.2*X*0.05 - Shyam selling price

1.2*X*0.05 = 504

X = Rs 400 is the cost of an article for Ram

Hope it Helps!!!!

20 points please help me I'm desperate and I will mark brainlyist

Answers

Answer:

  (a) 48, 52, 54

  (b) 6

  (c) b, c

Step-by-step explanation:

The sample mean is the mean of the sample. The range of sample means is the difference between the largest and smallest. As with all sampling processes, more data gives a better estimate.

(a)

The sample means are calculated in the attachment. For the different samples, they are ...

485254

(b)

The range of the sample means is the difference between the largest and the smallest:

  range = 54 -48 = 6

(c)

More data is better, and the closer the estimates are to each other, the better confidence they offer. The true statements are ...

A single sample mean will tend to be a worse estimate than the mean of the sample means.The closer the range of sample means is to zero, the more confident they can be in their estimate.

Find the output, y, when the input, x, is -5.

Answers

The output, y, when the input, x, is -5 is -2

How to determine the value of the output y?

The input is given as:

-5

This means that

x = -5

This is so because x represents the input

From the graph, we have the following highlight

The line of the graph passes through the point x = -5

On the graph;

When x = -5, the value of y is -2

This means that the output, y, when the input, x, is -5 is -2

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My neighbor just got two new cats and now she has more than 5 cats. How many cats did she have before?

Answers

The number of cats is an illustration of inequalities and your neighbor has 4 cats before she bought the 2 new cats

What are inequalities?

Inequalities are expressions, numbers and mathematical statements that have unequal values when compared and/or evaluated

How to determine the number of cats?

We start by representing the initial number of cats with x.

From the question, the new cats she bought are

New = 2

So, we have

x + New greater than 5


Rewrite properly as

x + New > 5

Substitute known values in the above inequality

x + 2 > 5

Subtract 2 from both sides

x + 2 - 2 > 5 - 2

Evaluate the right-hand side

x + 2 - 2 > 3

Evaluate the left-hand side

x > 3

The smallest integer number greater than 3 is 4

Hence, your neighbor has 4 cats before she bought the 2 new cats

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What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from a) 5 to 11? b)2 to 8? c)10 to 1?

Answers

Answer: 1/2, 1/2, 1/4

Step-by-step explanation:

To find the fraction that the hour hand turns of a clockwise revolution, we have to find how long it is going then divide by 12

Ex. a) 11 - 5 = 6, 6/12 = 1/2 so the hour hand turns by 1/2 of a clockwise revolution

b) 8 - 2 = 6, 6/12 = 1/2 so the hour hand turns by 1/2 of a clockwise revolution

c) For this, we have to convert 1 into 13 as 1 - 10 is a negative number

13 - 10 = 3, 3/12 = 1/4 so the hour hand turns by 1/4 of a clockwise revolution

The answers are :

a) 1/2

b) 1/2

c) 1/4

To find the fraction of a clockwise revolution, take the ratio between hours covered and hours covered in one revolution.

a)

Hours covered between 5 and 11 ⇒ 11 - 5 = 6Hours covered in 1 revolution ⇒ 126/12 = 1/2

b)

Hours covered between 2 and 8 ⇒ 8 - 2 = 6Hours covered in 1 revolution ⇒ 126/12 = 1/2

c)

Hours covered between 10 and 1 ⇒ 13 - 10 = 3 (∴ 12 + 1 = 13)Hours covered in 1 revolution ⇒ 123/12 = 1/4

What is the missing factor in this factor tree? 30 2x?

Answers

Answer:

15?

Step-by-step explanation:

2×15=30 i am not fully sure but this should be it

What is the value of x in the equation x-3y = 30, when y = 15?
1
04
8
80
200

Answers

Answer:

x = 75

Step-by-step explanation:

Given information from the question:

x - 3y = 30

y = 15

We can substitute y = 15 into the equation to find x.

x - 3(15) = 30

x - 45 = 30

x - 45 + 45 = 30 + 45

x = 75

Answer:

75

Step-by-step explanation:

x-3y=30

x-3×15=30

x-45=30

x=30+45

x=75

the mean change after 5 days is -0.01 inch what is the change on the fifth day? days: -0.05, 0.09, -0.04, and -0.08

Answers

Answer:

.06

Step-by-step explanation:

add all the 4 values listed, plus the .06

divide by 5

you get -.01

:)

43% of a sample of 100 visitors to a national park believes that additional funds should be used to preserve endangered species. what is the margin of sampling error for a 95% confidence interval?

Answers

The margin of sampling error for a 95% confidence interval is 9.7%

How to find the Margin of Error?

The formula for margin of error here is;

E = z√(p(1 - p)/N)

where;

n is sample size

z is the z score

p is the sample proportion

z-score for a 95% confidence interval from tables is 1.96.

We are given;

p = 43% = 0.43

n = 100

Thus;

E = 1.96√(0.43(1 - 0.43)/100)

E =  0.097 = 9.7%

Thus, we can conclude that  the margin of sampling error for a 95% confidence interval is 9.7%

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Can anyone help me with this!​

Answers

Answer:

The answer is B.

[tex] \frac{1025}{4} [/tex]

Step-by-step explanation:

Greetings !

[tex] \frac{x {}^{6} - x}{4y} ...substitute \: x = - 4 \: and \: y = 4 \\ \frac{( - 4) {}^{6} - (- 4) }{4(4)} ...apply \: exponent \: rule \\ \frac{4096 + 4}{16} = \frac{4100}{16} = \frac{1025}{4} [/tex]

(-4)^6 - - 4 / 4 x 4

4096 + 4 / 16

4100/16

= 1025/4

So, answer is B. 1025/4

Hope this helps!

Write the following as an inequality:

x is less than or equal to negative 3 or greater than or equal to 4

Answers

The become in the inequality form is -3≥x≥4.

According to the statement

we have given that the statement and we have to write this condition in the form of the inequality.

So, we know that the

Inequality, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

It is represented with the grater than or less than or equal to signs.

so, the given statement is

x is less than or equal to negative 3 or greater than or equal to 4

and we have to write in the inequality condition so,

we have to write it but before this break the statement like

x is less than or equal to negative 3

And

x is greater than or equal to 4.

So,

-3≥x≥4.

So, The become in the inequality form is -3≥x≥4.

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A
(5x − 3)°
B
E
(7x+15)°
D
(6y + 7)°
C

Answers

Answer:

The value of x = 14 ...

The value of ∠AED = ( 7x + 15) = 7(14) + 15 = 113

The value of ∠AEB = 5x-3 = 5(14) -3 = 67

Step-by-step explanation:

=> ∠BEC = ∠AED { vertically opposite angles }

∠AED = (7x + 15)°

=> ∠AEB + ∠BEC = 180° { linear pair }

=> ( 5x-3) + ( 7x+15) = 180°

=> 5x -3 + 7x + 15 = 180°

=> 12x + 12 = 180°

=> 12( x +1 ) = 180°

=> x+1 = 180/12

=> x +1 = 15

=> x = 15-1

=> x = 14

Find the radius of convergence R, then determine the interval of convergence

Answers

By the ratio test, the series converges for all [tex]x[/tex], since

[tex]\displaystyle \lim_{k\to\infty} \left|\frac{(k+1)^2 x^{k+4}}{(k+1)!} \cdot \frac{k!}{k^2 x^{k+3}}\right| = |x| \lim_{k\to\infty} \frac{(k+1)^2 k!}{k^2 (k+1)!} = |x| \lim_{k\to\infty} \frac1{k+1} = 0 < 1[/tex]

Then the radius of convergence is R = ∞, and the interval of convergence is the entire real line, -∞ < x < ∞.

The radius of convergence R isand the interval of convergence is (-∞, ∞) for the given power series. This can be obtained by using ratio test.  

Find the radius of convergence R and the interval of convergence:

Ratio test is the test that is used to find the convergence of the given power series.  

First aₙ is noted and then aₙ₊₁ is noted.

For  ∑ aₙ,  aₙ and aₙ₊₁ is noted.

[tex]\lim_{n \to \infty} | \frac{a_{n+1} }{a_{n} } |[/tex] = β

If β < 1, then the series convergesIf β > 1, then the series divergesIf β = 1, then the series inconclusive

Here aₙ = (n²/n!) xⁿ⁺³  and  aₙ₊₁ = ((n+1)²/(n+1)!) xⁿ⁺¹⁺³ = ((n+1)²/(n+1)!) xⁿ⁺⁴

Now limit is taken,

[tex]\lim_{n \to \infty} | \frac{a_{n+1} }{a_{n} } |[/tex] = [tex]\lim_{n \to \infty} | \frac{((n+1)^{2} /(n+1)!) x^{n+4} }{(n^{2} /n!) x^{n+3} } |[/tex]

                      = [tex]\lim_{n \to \infty} | \frac{((n+1)^{2} ) n!x^{n+4} }{(n+1)!(n^{2} ) x^{n+3} } |[/tex]

                      = [tex]\lim_{n \to \infty} | \frac{((1+1/n)^{2} ) x }{(n+1)} |[/tex]  

                      =   [tex]\lim_{n \to \infty} | \frac{ x }{(n+1)} |[/tex]  = 0 < 1

Since the limit is less than 1 the series is converging.

We get that,

interval of convergence = (-∞, ∞)

radius of convergence R =

Hence the radius of convergence R isand the interval of convergence is (-∞, ∞) for the given power series.

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PLEASE HELP IM STUCK

Answers

The number of outcomes possible from flipping each coin is 2, therefore;

The expression that can be used to find the number of outcomes for flipping 4 coins is: 2•2•2•2

How can the expression for the number of combinations be found?

The possible outcome of flipping 4 coins is given by the sum of the possible combinations of outcomes as follows;

The number of possible outcome from flipping the first coin = 2 (heads or tails)

The outcomes from flipping the second coin = 2

The outcome from flipping the third coin = 2

The outcome from flipping the fourth coin = 2

The combined outcome is therefore;

Outcome from flipping the 4 coins = 2 × 2 × 2 × 2

The correct option is therefore;

2•2•2•2

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30 points.
Please quick help

Answers

Using translation concepts, the expression for h(x) is given as follows:

[tex]h(x) = \sqrt{x + 4} - 1[/tex]

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the parent function is:

[tex]f(x) = \sqrt{x}[/tex]

For the translations, we have that:

It was shifted 4 units right, hence x -> x + 4.It was shifted 1 unit down, hence y -> y - 1.

Then the expression for h(x) is given as follows:

[tex]h(x) = \sqrt{x + 4} - 1[/tex]

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A star system with more than 2 but less than a million stars. which type of star system is pictured?

Answers

The star system is pictured is  open cluster

What is Open cluster?

A type of star cluster known as an open cluster is composed of up to a few thousand stars that are around the same age and originated from the same massive molecular cloud. Within the Milky Way galaxy, more than 1,100 open clusters have been found, and it is believed that there are many more.

What is solar system?

The Sun and the things that circle it make up the gravitationally bound solar system. It was created 4.6 billion years ago when a massive interstellar molecular cloud collapsed because to gravity. The Sun is the system's primary mass source, while Jupiter is home to the majority of the system's leftover mass.

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I understand that the question you are looking for is :

| Will mark brainliest | Which type of star system is pictured? |

A. globular cluster

B. open cluster

C. binary

Answer:

B

Step-by-step explanation:

open cluster

Mar18/Q9 - V2
2^p=1\8^4
Find the value of p.

Answers

Answer:

-12

Step-by-step explanation:

2^p = ⅛⁴

⅛ x ⅛ x ⅛ x ⅛ = 1/4096

2^p = 4096

log base 2 of 1/4096 = -12

Systems requests do not deal with factors involved in improving service.

a. true
b. false

Answers

Systems requests do not deal with factors involved in improving service: false

please answer these questions

Answers

Answer:12

Step-by-step explanation:

Answer:

8.  -3, 16

9.  -3, 4.5

Step-by-step explanation:

See attached worksheet.

Mean: about 25.1

Standard deviation: about 2.4
What is the z-score of the value 29,rounded to the nearest tenth

Answers

The z-score to the normal distribution table is 1.625

z-score of distribution table

The standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured.

The formula for calculating the z-score is expressed as;

z = x-μ/σ

where

μ is the mean of the data

σ is the standard deviation

x is the value

Given the parameters

μ = 25.1

σ = 2.4

x = 29

Substitute the given parameters

z = 29-25.1/2.4

z = 3.9/2.4

z = 1.625

Hence the z-score to the normal distribution table is 1.625

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The probability that a rental car will be stolen is. 4. if 3500 cars are rented, what is the approximate poisson probability that 2 or fewer will be stolen?

Answers

Using the Poisson distribution, there is a 0.8335 = 83.35% probability that 2 or fewer will be stolen.

What is the Poisson distribution?

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.

The probability that a rental car will be stolen is 0.0004, hence, for 3500 cars, the mean is:

[tex]\mu = 3500 \times 0.0004 = 1.4[/tex]

The probability that 2 or fewer cars will be stolen is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-1.4}1.4^{0}}{(0)!} = 0.2466[/tex]

[tex]P(X = 1) = \frac{e^{-1.4}1.4^{1}}{(1)!} = 0.3452[/tex]

[tex]P(X = 2) = \frac{e^{-1.4}1.4^{2}}{(2)!} = 0.2417[/tex]

Then:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2466 + 0.3452 + 0.2417 = 0.8335[/tex]

0.8335 = 83.35% probability that 2 or fewer will be stolen.

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Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. The system of equations models the total costs for each.

y = 7.5x

y = 5.5x + 10

1. Substitute: 7.5x = 5.5x + 10

How many classes could Anna take so that the total cost for the month would be the same?

classes

What is the total monthly cost when it is the same for both gyms?

Answers

The number of classes Anna can take so the total cost for the month will be the same is 5.

The monthly cost would be  $37.50.

When would the total cost be the same?

When the monthly cost is equal, both equations would be equal: 7.5x = 5.5x + 10

In order to determine the value of x, take the following steps:

Combine similar terms: 7.5x - 5.5x = 10 Add similar terms: 2x = 10 Divide both sides by 2 : 10 /2 = 5

Monthly cost when the cost is the same: 7.5 x 5 = $37.50

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Answer:

5 classes

37.50

Step-by-step explanation:

got it right on edge

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